DIFFUSION TENSOR IMAGING Marija Cauchi and Kenji Yamamoto.
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Transcript of DIFFUSION TENSOR IMAGING Marija Cauchi and Kenji Yamamoto.
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DIFFUSION TENSOR IMAGING
Marija Cauchi and Kenji Yamamoto
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Overview
Introduction
Pulse gradient spin echo
ADC/DWI
Diffusion tensor
Diffusion tensor matrix
Tractography
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DTI
• Non invasive way of understanding brain structural connectivity
• Macroscopic axonal organization• Contrast based on the directional rate of
diffusion of water molecules
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DTI
• WATER protons = signal in DTI• Diffusion property of water molecules (D)• D = diffusion constant • Move by Brownian motion / Random thermal
motion• Image intensities inversely related to the
relative mobility of water molecules in tissue and the direction of the motion
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Brownian motion of water molecule
Rosenbloom et al
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DIFFUSION
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Pulsed Gradient Spin-echo
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ω = ϒ B
•ω = angular frequency•ϒ = gyromagnetic ratio•B = (B0 + G * distance) = magnitude of the magnetic field
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What is b?
• b-value gives the degree of diffusion weighting and is related to the strength and duration of the pulse gradient as well as the interval between the gradients
• b changes by lengthening the separation of the 2 gradient pulses more time for water molecules to move around more signal loss (imperfect rephasing)
• G= gradient amplitude• δ = duration• = trailing to leading edge separation
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Apparent Diffusion Coefficient
• ADC – less barriers• ADC - more barriers
b-value
S
ADCbSS exp0
b-value
ln(S)
ADCbSS 0lnln
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ADC
• Dark regions – water diffusing slower – more obstacles to movement OR increased viscosity
• Bright regions – water diffusing faster
• Intensity of pixels proportional to extent of diffusion
• Left MCA stroke:
www.radiopaedia.org
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DWI
• Bright regions – decreased water diffusion
• Dark regions – increased water diffusion
www.radiopaedia.org
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DWI ADC
Hygino da Cruz Jr, Neurology 2008
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Colour FA map
• Colour coding of the diffusion data according to the principal direction of diffusion
• red - transverse axis (x-axis)• blue – superior-inferior (z -axis)• green – anterior-posterior axis
(y-axis)• Intensity of the colour is
proportional to the fractional anisotropy
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Water diffusion in brain tissue
• Depends upon the environment:- Proportion of intracellular vs extracellular
water: cytotoxic vs vasogenic oedema- Extracellular structures/large molecules
particularly in disease states- Physical orientation of tissue e.g.nerve fibre
direction
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Diffusion anisotropy
Diffusion is greater in the axis
parallel to the orientation of the
nerve fibre
Diffusion is less in the axis
perpendicular to the nerve fibre
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Effect of Varying Gradient direction
DWI z DWI x DWI y
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What is the diffusion tensor?• In the case of anisotropic diffusion: we fit a
model to describe our data: TENSOR MODEL
- This characterises diffusion in which the displacement of water molecules per unit time is not the same in all directions
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What is the diffusion tensor?
Johansen-Berg et al.Ann Rev. Neurosci 32:75-94 (2009)
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What is the diffusion tensor matrix?
• This is a 3 x 3 symmetrical matrix which characterises the displacement in three dimensions :
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The Tensor Matrix
S = S0e(-bD)
S = S0e(-bxxDxx-2bxyDxy-2bxzDxz-byyDyy-2byzDyz-bzzDzz)
For a single diffusion coefficient, signal= For the tensor matrix=
S/S0 =
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`Diffusion MRI` Johansen-Berg and Behrens
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Eigenvectors and Eigenvalues
• The tensor matrix and the ellipsoid can be described by the:
1. Size of the principles axes = Eigenvalue
2. Direction of the principles axes = Eigenvector
• These are represented by
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The Tensor Matrix
• λ1, λ2 and λ3 are termed the diagonal values of the tensor • λ1 indicates the value of maximum diffusivity or primary
eigenvalue (longitudinal diffusivity)• λ2 and λ3 represent the magnitude of diffusion in a plane
transverse to the primary one (radial diffusivity) and they are also linked to eigenvectors that are orthogonal to the primary one
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Indices of DiffusionSimplest method is the MEAN DIFFUSIVITY (MD):
l1+l2+l3MD = <l> = 3
- This is equivalent to the orientationally averaged mean diffusivity
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Indices of Anisotropic Diffusion• Fractional anisotropy (FA):
The calculated FA value ranges from 0 – 1 :
FA= 0 → Diffusion is spherical (i.e. isotropic)FA= 1 → Diffusion is tubular (i.e. anisotropic)
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Colour FA Map
Demonstrates the direction of fibres
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Tractography - Overview• Not actually a measure of individual axons, rather the data
extracted from the imaging data is used to infer where fibre tracts are
• Voxels are connected based upon similarities in the maximum diffusion direction
•
Johansen-Berg et al.Ann Rev. Neurosci 32:75-94 (2009)
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Tractography – Techniques
Degree of anisotropy Streamline tractography Probabilistic tractography
Nucifora et al. Radiology 245:2 (2007)
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Streamline (deterministic) tractography
• Connects neighbouring voxels from user defined voxels (SEED REGIONS) e.g. M1 for the CST
• User can define regions to restrict the output of a tract e.g. internal capsule for the CST
• Tracts are traced until termination criteria are met (e.g. anisotropy drops below a certain level or there is an abrupt angulation)
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Probabilistic tractography• Value of each voxel in the map = the probability
the voxel is included in the diffusion path between the ROIs
• Run streamlines for each voxel in the seed ROI• Provides quantitative probability of connection at
each voxel • Allows tracking into regions where there is low
anisotropy e.g. crossing or kissing fibres
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Crossing/Kissing fibres
Crossing fibres Kissing fibres
Low FA within the voxels of intersection
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Crossing/Kissing fibres
Assaf et alJ Mol Neurosci 34(1) 51-61 (2008)
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DTI - Tracts
Nucifora et al. Radiology 245:2 (2007)
Corticospinal Tracts -ProbabilisticCorticospinal Tracts - Streamline